In physical SI units, we have the relation $\widehat{p}={\widehat{k}}_{\mathrm{B}}/{\widehat{m}}_{\mathrm{u}}\widehat{\rho }\widehat{T}$, where the Boltzmann constant ${\widehat{k}}_{\mathrm{B}}\doteq 1.38\times {10}^{-23}\mathrm{J}/\mathrm{K}$ and the atomic unit mass ${\widehat{m}}_{\mathrm{u}}\doteq 1.66\times {10}^{-27}\mathrm{kg}$.

A similar approach was used also in the case of a globally neutral magnetized fluid (plasma) circling in strong gravitational field and toroidal magnetic field [36].

Rewriting relation (63) into the form $e^h{U}_t=\text{const}$, we can note the correspondence with one of the important results of the work [29]—relation (20). The correspondence is obvious; nevertheless, the authors consider a little bit different scenario from the one presented here. For instance, the differences are the rotation of the dipole magnetic field, constant specific charge of the matter, rigid co-rotation of the matter with the magnetic field, nonzero conductivity and a slightly different thermodynamical setup.

In the case $\ell =\text{const}$, the angular term in the pressure equations (38) vanishes, and in the case $\omega =\text{const}$, we have the condition $\omega =\omega (\ell )$ satisfied. Thus, in both the cases we can advantageously use the solution of the pressure equations in the united form (53), assuming that the correction function must be chosen as a function of ${\mathcal{A}}_{\varphi }$.

Note that in the original works of M. Abramowicz and his co-workers, the potential $\tilde{H}$ is denoted as $W$.

Note that the masses and radii of neutron stars are generally assumed in the ranges $1{\widehat{M}}_{\odot }\le \widehat{M}\le 3{\widehat{M}}_{\odot }$ and $3\overline{M}\le \overline{\mathcal{R}}\le 10\overline{M}$ [43]; magnetic fields reach their strengths $\widehat{\mathcal{B}}={10}^{10}\mathrm{T}$ [44]. The precise determination of the mentioned limits, however, is still of high interest, being very complex, dependent on the considered equation of state, etc.

The coupled simultaneously existing tori with a common cusp discussed here reminds us of the similar so-called ring equilibrium configuration of the neutral fluid discussed in papers [48, 49], there caused by the rotation of the central object and the chosen different angular momentum of the multiple tori. Here, a different physical ground for this effect occurs—- the additional electromagnetic interaction.